Astrometric calibration for all-sky cameras revisited

Context. Several fireball networks deploy all-sky cameras for the observation of bright meteors and bolides. Because the field is heavily distorted, a dedicated astrometric reduction is needed. A precise computation of the astrometric solution is essential to determine reliable orbital elements of the parent body and to recover possible fragments on ground.Aims. The purpose of this article is to assess the astrometric performances of this type of instruments, which is characterized by a wide field of view and small apertures. The currently available parametric models show a high level of complexity and generally suffer from parameter crosstalk and local minimum confinement if the initial estimates are not precisely provided. We address these issues here and propose a solution by adopting a new explicit parametrisation.Methods. The mismatch between the optical axis and the local zenith direction requires a geometric description that includes two centres of symmetry that lie very close to each other on the focal plane, causing an unreliable estimate of the related parameters. The introduction of new physical coordinates overcomes these issues, allowing a direct and independent estimation. We assessed the performances of different centroiding algorithms in the experimental conditions of an undersampled point spread function of reference stars and saturated bolides on video records. We implemented the algorithm for an automatic identification of bright sources on calibration frames and subsequent correlation with catalogue positions using astrometric projections of increasing complexity.Results. The algorithm and the new parametrisation of the astrometric solution are tested against real data from the PRISMA Italian fireball network and ensure good convergence properties for all cameras we tested so far. By processing astrometric data with a few months' statistics, we can achieve a random projection indeterminacy of the order of 10 arcsec, which is negligible with respect to single measurement errors on the bolide position.